Question

line t passes through (4, 5) and is perpendicular to the line shown on the coordinate grid.

Explanation:

Step1: Find slope of given line

The given line passes through $(0,3)$ and $(7,2)$. Slope formula: $m_1=\frac{y_2-y_1}{x_2-x_1}$
$m_1=\frac{2-3}{7-0}=-\frac{1}{7}$

Step2: Find slope of perpendicular line

Perpendicular slopes multiply to $-1$. So $m_2 \times m_1 = -1$
$m_2 = \frac{-1}{-\frac{1}{7}}=7$

Step3: Use point-slope form for line t

Point-slope formula: $y-y_1=m(x-x_1)$, using $(4,5)$ and $m_2=7$
$y-5=7(x-4)$

Step4: Simplify to slope-intercept form

Expand and isolate $y$:
$y-5=7x-28$
$y=7x-28+5$
$y=7x-23$

Answer:

The equation of line $t$ is $\boldsymbol{y=7x-23}$