Write the slope-intercept equation of the function whose graph satisfies the given conditions.
The graph of passes through and is perpendicular to the line that has an -intercept of 5 and
a -intercept of -15 .
The equation of the function is
(Use integers or fractions for any numbers in the equation.)

Ask by Knight Garza. in the United States

Mar 09,2025

Question

Write the slope-intercept equation of the function whose graph satisfies the given conditions.
The graph of passes through and is perpendicular to the line that has an -intercept of 5 and
a -intercept of -15 .
The equation of the function is
(Use integers or fractions for any numbers in the equation.)

Ask by Knight Garza. in the United States

Mar 09,2025

UpStudy AI · Accepted Answer

1. Find the slope of the given line using its intercepts. The line has an $$ x $$-intercept at $$ (5,0) $$ and a $$ y $$-intercept at $$ (0,-15) $$. The slope $$ m $$ of the line is given by

$$
m = \frac{0 - (-15)}{5 - 0} = \frac{15}{5} = 3.
$$

2. The slope of a line perpendicular to this line is the negative reciprocal of $$ 3 $$. Therefore, the perpendicular slope is

$$
-\frac{1}{3}.
$$

3. The function $$ f $$ passes through $$ (-9,8) $$ and has a slope of $$ -\frac{1}{3} $$. Using the point-slope form of the line,

$$
y - y_1 = m(x - x_1),
$$

we substitute $$ (x_1,y_1) = (-9,8) $$ and $$ m = -\frac{1}{3} $$:

$$
y - 8 = -\frac{1}{3}(x - (-9)) = -\frac{1}{3}(x + 9).
$$

4. Distribute the slope on the right-hand side:

$$
y - 8 = -\frac{1}{3}x - 3.
$$

5. Solve for $$ y $$ by adding 8 to both sides:

$$
y = -\frac{1}{3}x - 3 + 8,
$$

$$
y = -\frac{1}{3}x + 5.
$$

The equation of the function is

$$
y = -\frac{1}{3}x + 5.
$$
The equation of the function is $$ y = -\frac{1}{3}x + 5 $$.

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