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Chapter 2: Q49. (page 73)

Graph the line that satisfies each set of conditions.

Perpendicular to graph of 3x-2y=24intersects that graph at its

x- intercept.

Short Answer

Expert verified

The required graph for the given equation with intercepts is,

Step by step solution

01

Step 1. Determining the points which satisfy the equation 3x-2y=24.

The equation 3x-2y=24in slope- intercept form is

y=32x-12

So, the slope is 32and y- intercept is -12

So, (0,-12) satisfy the equation.

Wheny=0in the given equation,

3x-2y=243x=24x=8

So, other point is (8,0)

02

Step 2. Determining the slope of the line that is perpendicular to given line

Slope of given line = 32

Slope of line perpendicular to this line = -23.

03

Step 3. Determine the y-intercept.

The slope intercept form of line is

y=mx+c

Since, m=-23or,y=-23x+c

Since, the line passes through (8,0).

So,

0=-23脳8+cc=-163

Hence, the new equation formed is

y=-23x-163

04

Step 4. Concept of finding the points which satisfy the equations

Substitute x=0 in each equations and find the value of yand similarly put y=0 in each equations and find the value of x.

05

Step 5. Determining the point which satisfies the equations.

(0,-163) and (-8,0) satisfy the equation y=-23x-163

06

Step 6. Plotting the graph.

The obtained graph from the given equation is,

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