Question

What is an equation of a line, in point-slope form, that passes through (1, −7) and has a slope of −23 ?

y+7=−23(x−1)
y+7=23(x+1)
y−7=23(x−1)
y−7=−23(x+1)



What is the equation of a line, in point-slope form, that passes through (−2, −6) and has a slope of 13 ?

y+2=13(x+6)
y−2=13(x−6)
y+6=13(x+2)
y−6=13(x−2)

What is the equation in point-slope form of a line that passes through the points (−4, −1) and (5, 7) ?

y+4=98(x+1)
y−1=89(x−4)
y+1=87(x+4)
y+1=89(x+4)

What is the equation in point-slope form of a line that passes through the points (5, −3) and (−2, 9) ?

y−3=−2(x+5)
y+3=−2(x−5)
y−3=−127(x+5)
y+3=−127(x−5)

Answer 1

The point-slope form:

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

1.

$(1,\ -7)\to x_1=1,\ y_1=-7\\\\m=-\dfrac{2}{3}\\\\y-(-7)=-\dfrac{2}{3}(x-1)\\\\\boxed{y+7=-23(x-1)}$

2.

$(-2,\ -6)\to x_1=-2,\ y_1=-6\\\\m=13\\\\y-(-6)=13(x-(-2))\\\\\boxed{y+6=13(x+2)}$

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$m=\dfrac{y_2-y_1}{x_2-x_1}$

3.

$(-4,\ -1)\to x_1=-4,\ y_1=-1\\(5,\ 7)\to x_2=5,\ y_2=7\\\\m=\dfrac{7-(-1)}{5-(-4)}=\dfrac{8}{9}\\\\y-(-1)=\dfrac{8}{9}(x-(-4))\\\\\boxed{y+1=\dfrac{8}{9}(x+4)}$

4.

$(5,\ -3)\to x_1=5,\ y_1=-3\\(-2,\ 9)\to x_2=-2,\ y_2=9\\\\m=\dfrac{9-(-3)}{(-2)-5}=\dfrac{12}{7}\\\\y-(-3)=\dfrac{12}{7}(x-5)\\\\\boxed{y+3=\dfrac{12}{7}(x-5)}$