Question

write the point - slope form of the line satisfying the given conditions. then use the point - slope form of the equation to write the slope - intercept form of the equation. slope = 3, passing through (-5,6) type the point - slope form of the equation of the line. (simplify your answer. use integers or fractions for any numbers in the equation)

Explanation:

Step1: Recall point-slope formula

The point-slope form of a line is $y - y_1 = m(x - x_1)$, where $m$ is the slope, and $(x_1, y_1)$ is a point on the line.

Step2: Substitute given values

Here, $m=3$, $x_1=-5$, $y_1=6$. Substitute into the formula:
$y - 6 = 3(x - (-5))$
Simplify the sign inside the parentheses:
$y - 6 = 3(x + 5)$

Step3: Convert to slope-intercept form

Expand the right-hand side:
$y - 6 = 3x + 15$
Add 6 to both sides to solve for $y$:
$y = 3x + 15 + 6$
$y = 3x + 21$

Answer:

Point-slope form: $y - 6 = 3(x + 5)$
Slope-intercept form: $y = 3x + 21$