Question

use the given conditions to write an equation for the line in point - slope form and in slope - intercept form. passing through (4,4) with x - intercept 1

Explanation:

Step1: Identify two points

The line passes through $(4,4)$ and its x-intercept is 1, so the second point is $(1,0)$.

Step2: Calculate the slope

Slope formula: $m=\frac{y_2-y_1}{x_2-x_1}$
$m=\frac{4-0}{4-1}=\frac{4}{3}$

Step3: Write point-slope form

Use point $(4,4)$: $y-y_1=m(x-x_1)$
$y-4=\frac{4}{3}(x-4)$

Step4: Convert to slope-intercept form

Expand and solve for $y$:
$y-4=\frac{4}{3}x-\frac{16}{3}$
$y=\frac{4}{3}x-\frac{16}{3}+4$
$y=\frac{4}{3}x-\frac{16}{3}+\frac{12}{3}$
$y=\frac{4}{3}x-\frac{4}{3}$

Answer:

Point-slope form: $y-4=\frac{4}{3}(x-4)$
Slope-intercept form: $y=\frac{4}{3}x-\frac{4}{3}$