Mathematics: write the equation of the line that passes through the points (-3,4) and (-4,2). Write the final answer in slope intecept form

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write the equation of the line that passes through

kidkoolaidboy96291

10.02.2022

The equation in the slope-intercept form will be:

y=2x+10

Step-by-step explanation:

Given the points

(-3, 4)(-4, 2)

Finding the slope between two points

$\left(x_1,\:y_1\right)=\left(-3,\:4\right),\:\left(x_2,\:y_2\right)=\left(-4,\:2\right)$

$\mathrm{Slope}=\frac{y_2-y_1}{x_2-x_1}$

$m=\frac{2-4}{-4-\left(-3\right)}$

m=2

As the point-slope form of the line equation is

$y-y_1=m\left(x-x_1\right)$

putting the values m=2 and the point (-3, 4)

$y-4=2\left(x-\left(-3\right)\right)$

$y-4=2\left(x+3\right)$

Writing the equation in slope-intercept form

y=mx+b

where m is the slope, and b is the y-intercept

so the equation becomes

$y-4=2\left(x+3\right)$

add 4 to both sides

$y-4+4=2\left(x+3\right)+4$

y=2x+10

Therefore, the equation in the slope-intercept form will be:

y=2x+10

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