Question

write the equation of a line in slope - intercept form that has a slope of 7 and passes through the point (16, 17).
y = 7x + 15

y = -7x - 15

y = 7x - 95

y = -7x - 95

Explanation:

Step1: Recall slope - intercept form

The slope - intercept form of a line is $y = mx + b$, where $m$ is the slope and $b$ is the y - intercept. We know that $m = 7$, so the equation of the line is $y=7x + b$.

Step2: Substitute the point into the equation

We know that the line passes through the point $(x = 16,y = 17)$. Substitute $x = 16$, $y = 17$ and $m = 7$ into the equation $y=mx + b$:

$$17=7\times16 + b$$

Step3: Solve for $b$

First, calculate $7\times16=112$. Then the equation becomes:

$$17 = 112 + b$$

Subtract 112 from both sides of the equation:

$$b=17 - 112=- 95$$

Step4: Write the equation of the line

Since $m = 7$ and $b=-95$, the equation of the line in slope - intercept form is $y = 7x-95$.

Answer:

$y = 7x - 95$ (the option with the equation $y = 7x - 95$)