PSAT Math : Slope and Line Equations
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Example Questions
Example Question #1 :How To Find Slope Of A Line
Based on the table below, when x = 5, y will equal
x |
y |
-1 |
3 |
0 |
1 |
1 |
-1 |
2 |
-3 |
–11
–10
11
–9
–9
Use 2 points from the chart to find the equation of the line.
Example: (–1, 3) and (1, –1)
Using the formula for the slope, we find the slope to be –2. Putting that into our equation for a line we get y = –2x + b. Plug in one of the points for x and y into this equation in order to find b. b = 1.
The equation then will be: y = –2x + 1.
Plug in 5 for x in order to find y.
y = –2(5) + 1
y = –9
Example Question #1 :Geometry
What is the slope of a line that runs through points: (-2, 5) and (1, 7)?
2/3
2
5/7
3/2
2/3
The slope of a line is defined as a change in the y coordinates over a change in the x coordinates (rise over run).
To calculate the slope of a line, use the following formula:
Example Question #3 :Slope And Line Equations
A line passes through the points (–3, 5) and (2, 3). What is the slope of this line?
–2/5
2/3
–2/3
-3/5
2/5
–2/5
The slope of the line that passes these two points are simply ∆y/∆x = (3-5)/(2+3) = -2/5
Example Question #1 :How To Find Slope Of A Line
Which of the following lines intersects they-axis at a thirty degree angle?
y=x√3 + 2
y=x((√3)/3) + 1
y=x√2 - 2
y=x- √2
y=x
y=x√3 + 2
Example Question #5 :Slope And Line Equations
What is a possible slope of liney?
–2
2
–2
The slope is negative as it starts in quadrant 2 and ends in quadrant 4. Slope is equivlent to the change inydivided by the change inx. The change inyis greater than the change inx, which implies that the slope must be less than –1, leaving –2 as the only possible solution.
Example Question #6 :Slope And Line Equations
What is the slope between
Let
Example Question #1 :Lines
Example Question #1 :Geometry
Refer to above red line. What is its slope?
The slope of a line. given two points
Set
Example Question #9 :Slope And Line Equations
Which of the following equations has as its graph a line with slope 4?
None of the other responses is correct.
For each equation, solve for
Slope:
Slope:
Slope:
Slope:
The line of the equation
is the one with slope 4.
Example Question #1 :How To Find The Equation Of A Line
Solve the equation forxandy.
–x– 4y= 245
5x+ 2y= 150
x= 234/5
y= 1245/15
x= 3
y= 7
x= 545/9
y= –1375/18
x= –1375/9
y= 545/18
x= 545/9
y= –1375/18
While solving the problem requires the same method as the ones above, this is one is more complicated because of the more complex given equations. Start of by deriving a substitute for one of the unknowns. From the second equation we can derive y=75-(5x/2). Since 2y = 150 -5x, we divide both sides by two and find our substitution for y. Then we enter this into the first equation. We now have –x-4(75-(5x/2))=245. Distribute the 4. So we get –x – 300 + 10x = 245. So 9x =545, and x=545/9. Use this value for x and solve for y. The graph below illustrates the solution.
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