Answer :
When finding out slope, it may help to draw a black graph to answer any questions.
Slope is the rate that a line travels across the graph. Think of slope as a driveway. The really steep driveways, the ones that are fun ride down on bicycles but are hard to walk up, have a really steep slope. The ones that are nearly flat have a shallow slope.
The question tells you that the slope is 3 and the line passes through the point (-4,7). Then, it asks for point-slope form and the slope-intercept form.
First, let's focus on the slope-intercept form. The format for this equation is y=mx+b. The 'y' means the line, the 'm' means the slope (the 'x' is just there to show that it's the slope), and the 'b' is the point where the line crosses the y-axis (the horizontal line).
Since we know that the slope is 3, we can already fill in one of the blanks:
y=3x+b
On your blank graph, find the point (-4,7), which is in the upper left quadrant, four from the y-axis and seven from the x-axis. Using that point, draw a line that goes up 3 squares, and over 1 square. Continue this until the line crosses the y-axis.
Your line should have crossed the y-axis at (0,19). This means that the y-intercept is 19.
Your slope-int. equation is y=3x+19.
The equation for point-slope form is y-y₁=m(x-x₁).
The 'y' and the 'm' still stand for the same things, but the 'y₁' and the 'x₁' stand for the x and y coordinates.
Since we already know the coordinates, we can just plug in the information that we already have:
Your point-slope equation is y-7=3(x+4).
Slope is the rate that a line travels across the graph. Think of slope as a driveway. The really steep driveways, the ones that are fun ride down on bicycles but are hard to walk up, have a really steep slope. The ones that are nearly flat have a shallow slope.
The question tells you that the slope is 3 and the line passes through the point (-4,7). Then, it asks for point-slope form and the slope-intercept form.
First, let's focus on the slope-intercept form. The format for this equation is y=mx+b. The 'y' means the line, the 'm' means the slope (the 'x' is just there to show that it's the slope), and the 'b' is the point where the line crosses the y-axis (the horizontal line).
Since we know that the slope is 3, we can already fill in one of the blanks:
y=3x+b
On your blank graph, find the point (-4,7), which is in the upper left quadrant, four from the y-axis and seven from the x-axis. Using that point, draw a line that goes up 3 squares, and over 1 square. Continue this until the line crosses the y-axis.
Your line should have crossed the y-axis at (0,19). This means that the y-intercept is 19.
Your slope-int. equation is y=3x+19.
The equation for point-slope form is y-y₁=m(x-x₁).
The 'y' and the 'm' still stand for the same things, but the 'y₁' and the 'x₁' stand for the x and y coordinates.
Since we already know the coordinates, we can just plug in the information that we already have:
Your point-slope equation is y-7=3(x+4).
