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Writing Linear Equations
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Writing an Equation Given Two Points on the Line
Write the equation of the line that passes through the points (7,-4) and (-1,3), first in point-slope form, and then in
slope-intercept form.
The slope of the line is
When the point (7.-4) is used, the point-slope form of the line is
The slope-intercept form of the line is

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Answer:

[tex]\text{The slope:}\ m=-\dfrac{7}{8}\\\\\text{The point-slope form:}\ y+4=-\dfrac{7}{8}(x-7)\\\\\text{The slope-intercept form:}\ y=-\dfrac{7}{8}x+\dfrac{17}{8}[/tex]

Step-by-step explanation:

The slope-intercept form of an equation of a line:

[tex]y=mx+b[/tex]

m - slope

b - y-intercept

The point-slope form of an equation of a line:

[tex]y-y_1=m(x-x_1)[/tex]

m - slope

The formula of a slope:

[tex]m=\dfrac{y_2-y_1}{x_2-x_1}[/tex]

We have two points (7, -4) amd (-1, 3).

Calculate the slope:

[tex]m=\dfrac{3-(-4)}{-1-7}=\dfrac{7}{-8}=-\dfrac{7}{8}[/tex]

The point-slope form of an equation of a line:

[tex]y-(-4)=-\dfrac{7}{8}(x-7)\\\\y+4=-\dfrac{7}{8}(x-7)[/tex]

Convert to the slope-intercept form:

[tex]y+4=-\dfrac{7}{8}(x-7)[/tex]        use the distributive property

[tex]y+4=-\dfrac{7}{8}x+\dfrac{49}{8}[/tex]     subtract 4 = 32/8 from both sides

[tex]y=-\dfrac{7}{8}x+\dfrac{17}{8}[/tex]

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