Matching a Slope-Intercept Equation with Its Graph (3.10.4) Flashcards
• Slope-intercept equation of a line: y = mx + b. The constant, m, represents the slope or rate of change from one point
to the next in the line. The constant, b, represents the y-intercept or point where the line crosses the y-axis.
• Slope-intercept equation of a line: y = mx + b. The constant, m, represents the slope or rate of change from one point
to the next in the line. The constant, b, represents the y-intercept or point where the line crosses the y-axis.
• The point-slope form of an equation: y – y1 = m(x – x1
). This equation is created from the slope equation. It allows you
to create the equation of a line knowing any one point and the slope.
• The point-slope form of an equation: y – y1 = m(x – x1
). This equation is created from the slope equation. It allows you
to create the equation of a line knowing any one point and the slope.
Consider the example given here:
y + 1 =2( x + 1).
Notice, the equation is in point-slope form. The slope is 2
and the given point is (–1, –1).
Remember: Change the signs for the given point because
those coordinates are being subtracted in the formula.
This equation does not contain x. Therefore the slope is 0,
which makes it a horizontal line. Clearly the y-intercept is
at 3.
So, you graph a horizontal line at y = 3.
Choose any point on this line. The y can be anything in the
real numbers. The x = 1.
So, graphing the line shows you it is vertical.
Notice this equation has no y-term.
Solve it for x.
Graph it.
You’re done.
Consider the example given here:
y + 1 =2( x + 1).
Notice, the equation is in point-slope form. The slope is 2
and the given point is (–1, –1).
Remember: Change the signs for the given point because
those coordinates are being subtracted in the formula.
This equation does not contain x. Therefore the slope is 0,
which makes it a horizontal line. Clearly the y-intercept is
at 3.
So, you graph a horizontal line at y = 3.
Choose any point on this line. The y can be anything in the
real numbers. The x = 1.
So, graphing the line shows you it is vertical.
Notice this equation has no y-term.
Solve it for x.
Graph it.
You’re done.
First, solve this equation for y.
Then you see that your slope is 2/3, and your y-intercept is
–1/3.
Graph the line. First, locate your y-intercept. Then count up
2 and to the right 3 for the next point. Finally, draw the line.
First, solve this equation for y.
Then you see that your slope is 2/3, and your y-intercept is
–1/3.
Graph the line. First, locate your y-intercept. Then count up
2 and to the right 3 for the next point. Finally, draw the line.
