Math

Graphs of Functions

Slope Intercept

$y=mx+b$ or $y-y_1=\left(x-x_1\right)+b$

Vertical line: Slope is Undefined

Horizontal line: Slope is 0

Parallel lines: Slope is the same for both lines

Perpendicular lines: Slope of one is the inverse of the other

Ex: Line perpendicular to $y=\frac34x+8$ is $y=-\frac43x+8$

Ex: Distance between (-4, 3) & (5, -1)

$\frac{3-\left(-1\right)}{5-\left(-4\right)}=\frac49$

$3=-\frac49\left(-4\right)+b$

$3-\frac49\left(4\right)=b$

$b=3-\frac49\left(4\right)$

$b=\frac{11}{9}$

$y=\frac49x+\frac{11}{9}$

Finding the distance between 2 points

$d=\sqrt{\left(x_1+x_2\right)^2+\left(y_1+y_2\right)^2}$

Finding the midpoint between 2 points

$M=\left(\frac{x_1+x_2}{2},\frac{y_1+y_2}{2}\right)$

Practice Questions

Find an equation of the line that passes through the point (3, -4) and has a slope of m = 2

$y=mx+b$ | $y=2x+b$ | $-4=2\left(3\right)+b$ | $-4=6+b$ | $b=-10$

$y-y_1=m\left(x-x_1\right)$ | $y-\left(-4\right)=2\left(x-3\right)$ | $y+4=2\left(x-3\right)$ $y=2x-10$

Find an equation of the line passes through (1, 2) and (-3, -2)

$m=\frac{-4}{-4}=1$

$2=1+b$ | $b=1$

$y=x+1$

Find an equation of a horizontal line that passes through (-4, -3)

$y=0\left(x\right)-3$

$y=-3$

Find an equation of a vertical line that passes through (0, 5)

$m=undef$

$x=0$

Find an equation of the line that passes through the point (-2, 2) and is parallel to $2x-4y+8=0$

$2x-4y+8=0$ or $4y=3x+8$ or $y=\frac34x+2$

What is parallel?

$m=\frac34$

$2=\frac34\left(-2\right)+b$ | $2=-\frac62+b$ | $b=\frac72$

$y=\frac34x+\frac72$

Is the equation a linear function of x?

a) $2x+3y=6$

1: Yes

2: $y=-\frac23x+2$

b) $3\sqrt{x}+4y=0$

1: No

d) $\frac13x=\frac23y+\sqrt5$