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QuestionFind the intercepts of the line given by y−3=5(x−2)y-3=5(x-2). yy-intercept: xx-intercept:

Studdy Solution

STEP 1

Assumptions1. The equation of the line is given as y−3=5(x−)y-3=5(x-) . We are asked to find the y-intercept and the x-intercept of the line3. The y-intercept of a line is the point where the line crosses the y-axis, which is when x=04. The x-intercept of a line is the point where the line crosses the x-axis, which is when y=0

STEP 2

First, let's find the y-intercept. We do this by setting x=0 in the equation of the line.

STEP 3

Substitute x=0x=0 into the equation.
y−3=5(0−2)y-3=5(0-2)

STEP 4

implify the equation to find the y-coordinate of the y-intercept.
y−3=times−2y-3= \\times -2

STEP 5

olve for y.
y−3=−10y-3=-10

STEP 6

Add3 to both sides of the equation to isolate y.
y=−10+3y=-10+3

STEP 7

Calculate the y-coordinate of the y-intercept.
y=−7y=-7The y-intercept of the line is -7.

STEP 8

Now, let's find the x-intercept. We do this by setting y=0 in the equation of the line.

STEP 9

Substitute y=y= into the equation.
−3=5(x−2)-3=5(x-2)

STEP 10

implify the equation to find the x-coordinate of the x-intercept.
−3=5x−10-3=5x-10

STEP 11

Add10 to both sides of the equation to isolate the term with x.
−3+10=5x-3+10=5x

STEP 12

implify the left side of the equation.
7=5x7=5x

STEP 13

Divide both sides of the equation by5 to solve for x.
x=75x=\frac{7}{5}The x-intercept of the line is 75\frac{7}{5}.
So, the y-intercept is -7 and the x-intercept is 75\frac{7}{5}.

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