# Linear Equations in Slope Intercept Form Worksheet

Linear Equations in Slope Intercept Form Worksheet
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1.
What are the $x$ and $y$ intercepts of the line in the graph?

 a. $x$-intercept is - 2 and $y$-intercept is 2 b. $x$-intercept is - 2 and $y$-intercept is - 2 c. $x$-intercept is 2 and $y$-intercept is - 2 d. $x$-intercept is 2 and $y$-intercept is 2

#### Solution:

The x-intercept is the x-coordinate of the point where a line crosses the x-axis.

In the figure, the line crosses the x-axis at x = 2.

So, the x-intercept of the line is 2.

The y-intercept is the y-coordinate of the point where a line crosses the y-axis.

In the figure, the line crosses the y-axis at y = 2.

So, the y-intercept of the line is 2.

The x and y intercepts of the line are 2 and 2 respectively.

2.
Find the equation of a line whose slope is 4 and $y$-intercept is 5.
 a. $x$ = 5$y$ - 4 b. $y$ = 4$x$ + 5 c. $x$ = 4$y$ + 5 d. $y$ = 5$x$ - 4

#### Solution:

The equation of the line in slope intercept form with slope m and y-intercept b is y = mx + b.

y = (4)x + (5)
[Substitute m = 4 and b = 5.]

y = 4x + 5
[Simplify the equation.]

The equation of the line in slope-intercept form is y = 4x + 5.

3.
Write the equation of the line whose slope is -4 and $y$-intercept is - $\frac{2}{3}$.
 a. $y$ = 4$x$ - $\frac{2}{3}$ b. $y$ = 4$x$ + $\frac{2}{3}$ c. $y$ = -4$x$ - $\frac{2}{3}$ d. None of the above

#### Solution:

The equation of the line in slope-intercept form with slope m and y-intercept b is y = mx + b.

y = (-4)x + (- 23)
[Substitute m = - 4 and b = - 2 / 3.]

y = -4x - 23
[Simplify the equation.]

The equation of the line in slope-intercept form is y = -4x - 2 / 3.

4.
Is the equation $\frac{\left(x-1\right)}{1}$+ $\frac{\left(y-3\right)}{3}$= 24 + 42 in slope-intercept form?
 a. No b. Yes

#### Solution:

Compare the equation (x-1) / 1+ (y-3) / 3= 24 + 42 with the slope-intercept equation y = mx + b.

It is clear that the equation is not in the slope-intercept form.

5.
Identify the equation of the line in slope-intercept form for the graph shown.

 a. $y$ = $x$ - 3 b. $y$ = - $x$ - 3 c. $y$ = - $x$ + 3 d. $y$ = $x$ + 3

#### Solution:

The slope intercept form of the equation of a line with slope m and y-intercept b is y = mx + b.

From the graph, (x1, y1) = (3, 0) and (x2, y2) = (0, - 3).

Slope m = y2 -y1x2 -x1

m = - 3 - 00 - 3
[Substitute the values of x1, y1, x2 and y2.]

m = - 3- 3 = 1
[Simplify the fraction.]

The graph of the line crosses the y-axis at (0, - 3).

The y-intercept is the y-coordinate of the point where a line crosses the y-axis.

y-intercept, b = - 3

y = (1)x + (- 3)
[Substitute the values of m and b in step 1.]

y = x - 3
[Simplify the equation.]

The equation of the line in slope-intercept form is y = x - 3.

6.
Is the equation $y$ = 4$x$ + 3 in slope-intercept form?
 a. No b. Yes

#### Solution:

The slope-intercept form of the equation of a line with slope m and y-intercept b is y = mx + b.

The equation y = 4x + 3 is also in the same form as the equation in step 1, with slope 4 and y-intercept 3.

So, the equation y = 4x + 3 is in slope-intercept form.

7.
Find the slope of the line $y$ = $\frac{2}{3}$$x$ + $\frac{1}{3}$.
 a. $\frac{2}{3}$ b. $\frac{1}{3}$ c. $\frac{3}{4}$ d. None of the above

#### Solution:

The slope-intercept form of the equation of a line with slope m and y-intercept b is y = mx + b.

y = 23x + 13
[Given Equation.]

m = 23
[Compare the equation with slope-intercept form equation.]

The slope of the line is 2 / 3.

8.
What is the $y$-intercept of the line $y$ = $\frac{-\left(4x\right)}{5}$+ $\frac{5}{6}$?
 a. $\frac{4}{6}$ b. $\frac{5}{6}$ c. $\frac{4}{5}$ d. None of the above

#### Solution:

The slope-intercept form of the equation of a line with slope m and y-intercept b is y = mx + b.

y = -(4x) / 5+ 5 / 6
[Given Equation.]

b = 56
[Compare the equation with slope-intercept form equation.]

The y-intercept of the line is 5 / 6.

9.
What is the slope of the line in the graph?

 a. 2 b. -2 c. 3 d. -3

#### Solution:

From the graph, (x1, y1) = (-1,0) and (x2, y2) = (0,-2).

Slope m = (y2 - y1) / (x2 - x1)

m = (-2-0)[0-(-1)]
[Substitute the values of x1, y1, x2 and y2.]

m = -2
[Simplify the fraction.]

The slope of the line shown in the graph is -2.

10.
Write the $x$ and $y$ intercepts of the line AB.

 a. $x$-intercept is -3 and $y$-intercept is -3 b. $x$-intercept is -3 and $y$-intercept is 3 c. $x$-intercept is 3 and $y$-intercept is -3 d. None of the above

#### Solution:

The x-intercept is the x-coordinate of the point where a line crosses the x-axis.

In the figure, the line crosses the x-axis at x = -3.

So, the x-intercept of the line is -3.

The y-intercept is the y-coordinate of the point where a line crosses the y-axis.

In the figure, the line crosses the y-axis at y = 3.

So, the y-intercept of the line is 3.

The x and y intercepts of the line are -3 and 3.