Write an equation of the line passing through the point (5,3) with slope m = -4

Mathematics

2 answers:

ANEK [815]3 years ago

6 0

Answer:

Step-by-step explanation:

For this problem, point slope form would be the easiest.

Point Slope Form- y-y1 = m(x-x1)

In this case, y1 is 3, x1 is 5, and m would be the slope which is -4.

y-3=-4(x-5)

This is how to write an equation for the problem.

lord [1]3 years ago

3 0

Answer:

$\large{\boxed{y-3=-4(x-5)-\text{point-slope form}}\\\boxed{y=-4x+23}}$

Step-by-step explanation:

The equation of a line in point-slope form:

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

m - slope

(x₁, y₁) - point

We have the slope m = -4 and the point (5, 3). Substitute:

$y-3=-4(x-5)$ <em>use distributive property</em>

$y-3=-4x+(-4)(-5)$

$y-3=-4x+20$ <em>add 3 to both sides</em>

$y=-4x+23$

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$(\stackrel{x_1}{2}~,~\stackrel{y_1}{-50})\qquad (\stackrel{x_2}{4}~,~\stackrel{y_2}{-88}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{-88}-\stackrel{y1}{(-50)}}}{\underset{run} {\underset{x_2}{4}-\underset{x_1}{2}}}\implies \cfrac{-88+50}{2}\implies \cfrac{-38}{2}\implies -19$

$\begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{(-50)}=\stackrel{m}{-19}(x-\stackrel{x_1}{2}) \\\\\\ y+50=-19x+38\implies y=-19x-12$