b Start with the Slope Formula, then use that to create the slope-intercept form for each pair of coordinates.
C
c Start with the Slope Formula, then use that to create the slope-intercept form for each pair of coordinates.
A
a y=1/2x+4
B
b y=-3x+4
C
c y=-4+9
Practice makes perfect
a To determine the slope between a pair of points we use the Slope Formula. In this formula, x_1 and y_1 are coordinates of the first point, while x_2 and y_2 are coordinates of the second point.
m=y_2-y_1/x_2-x_1
This time we have a line that passes through (2,5) and (6,7). We will substitute x_1= 2, y_1= 5, x_2= 6, and y_2= 7 into the formula to find m.
We want to find the equation of the line passing through this pair of points. To do so, we will recall the slope-intercept form of a line.
y = mx+ b
In this equation, y and x are the coordinates of a point in the line, m is the slope, and b indicates the y-intercept. We will substitute m= 12, x= 2, and y= 5 into this formula to get a partial equation of the line.
y = mx+ b ⇓ 5=( 1/2)( 2)+ b
Let's solve for b!
Now that we know both the slope m and the y-intercept b we can write the complete equation of the line.
y= 1/2x+ 4
b We want to find the equation of the line passing through (- 4,16) and (3,- 5). To find it, we will start by finding the slope. Let's recall the Slope Formula.
m=y_2-y_1/x_2-x_1
We will substitute x_1= -4, y_1= 16, x_2= 3, and y_2= -5 into this formula and evaluate it for m.
Next, we will recall the slope-intercept form of the line.
y = mx+ b
We will substitute m= - 3, x= -4, and y= 16 into this equation to get a partial equation of the line.
y = mx+ b ⇓
16=( -3)( -4)+ b
As we can see, we need to find the value of the y-intercept. To find it, we will solve the above equation for b.
Since we want the equation of the line, we can recall the slope-intercept form of a line.
y = mx+ b
We will substitute m= - 4, x= - 2, and y= 17 into this equation to get a partial equation of the line.
y = mx+ b ⇓
17=( -4)( -2)+ b
Next, we will solve this equation to find the value of b. Let's do it!
