marleenmourad
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Please Help I Will Mark As Brainliest IF Answer Is Right Lt3 class=

Sagot :

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Answer:

[tex]y=\frac{7}{4}x-9[/tex]

Step-by-step explanation:

Question:

Find the equation of the line through the point (4, -2) with slope [tex]\frac{7}{4}[/tex]

Answer + Step-by-step explanation:

Answer: [tex]y=\frac{7}{4}x-9[/tex]

Step-by-step explanation:

When trying to find the equation of a line passing through a point and then given the slope, always remember if you're trying to write the equation in slope-intercept form, find the slope and the y-intercept of the equation.

Slope-Intercept form: y = mx + b where m = slope and b = y-intercept

so the slope is already given but we have to find the y-intercept.

so... the equation of the line with a slope of [tex]\frac{7}{4}[/tex] is:

[tex]y=\frac{7}{4}x[/tex]

but in addition, we need a y-intercept so...

[tex]y=\frac{7}{4}x+b[/tex]

now use the given point on the question "(4, -2)" to solve for the y-intercept

so plug in the coordinates of the point in the equation:

[tex]y=\frac{7}{4}x+b[/tex]

[tex](-2)=\frac{7}{4}(4)+b[/tex]

[tex]-2=\frac{28}{4} +b[/tex]

[tex]-2=7+b[/tex]

[tex]b=-2-7[/tex]

[tex]b=-9[/tex]

so the y-intercept of the line is -9

and the equation of the line is [tex]y=\frac{7}{4}x-9[/tex]

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