Question

Question 101 points)

Which equation in slope-intercept form represents the line that passes through (5, 1) and
(-4,7)


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Answer 1

`\large\boxed{y=-(2)/(3)x+(13)/(3)}`

Explanation:

`\text{The slope-intercept form of an equation of a line:}\\\\y=mx+b\\\\m-slope\\b-y-intercept\\\\\text{The formula of a slope:}\\\\m=(y_2-y_1)/(x_2-x_1)\\\\===============================`

`\text{We have the point:}\\\\(5,\ 1)\ \text{and}\ (-4,\ 7).\ \text{Substitute:}\\\\m=(7-1)/(-4-5)=(6)/(-9)=-(6:3)/(9:3)=-(2)/(3)\\\\\text{We have the equation in form:}\\\\y=-(2)/(3)x+b\\\\\text{Put the coordinates of the point (5, 1) to the equation:}\\\\1=-(2)/(3)(5)+b\\\\1=-(10)/(3)+b\qquad\text{add}\ (10)/(3)\ \text{to the both sides}\\\\(3)/(3)+(10)/(3)=b\to b=(13)/(3)\\\\\text{Finally:}\\\\y=-(2)/(3)x+(13)/(3)`