The other format for straight-line equations is called the "point-slope" form. For this one, they give you a point (x1, y1) and a slope m, and have you plug it into this formula:
y – y1 = m(x – x1)
the subscripts are just intended to indicate the point they give you. You have the "x" and "y" that are always in your equation, and then you have the specific x and y from the point they gave you. Here's how you use the point-slope formula:
ex:
Find the equation of the straight line that has slope m = 4 and passes throughthe point (–1, –6).
They've given me m = 4, x1 = –1, and y1 = –6. I'll plug these values into the point-slope form:
y – y1 = m(x – x1)
y – (–6) = (4)(x – (–1))
y + 6 = 4(x + 1)
y + 6 = 4x + 4
y = 4x + 4 – 6
y = 4x – 2
You can find the straight-line equation using the point-slope form if they just give you a couple points:
Find the equation of the line that passes through the points (–2, 4) and (1, 2).
Then I can use either point as my (x1, y1), along with this slope Ive just calculated, and plug in to the point-slope form. Using (–2, 4) as the (x1, y1), I get:
y – y1 = m(x – x1)
y – (4) = (– 2/3)(x – (–2))
y – 4 = (– 2/3)(x + 2)
y – 4 = (– 2/3)x – 4/3
y = (– 2/3)x – 4/3 + 4
y = (– 2/3)x – 4/3 + 12/3
y = (– 2/3)x + 8/3
