PSAT Math : Geometry
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Example Question #1 : Coordinate Geometry
Based on the table below, when x = 5, y will equal
|
x |
y |
|
-1 |
3 |
|
0 |
1 |
|
1 |
-1 |
|
2 |
-3 |
11
–9
–10
–11
–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 : Coordinate 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 #2 : Coordinate Geometry
A line passes through the points (–3, 5) and (2, 3). What is the slope of this line?
2/3
–2/5
–2/3
2/5
-3/5
–2/5
The slope of the line that passes these two points are simply ∆y/∆x = (3-5)/(2+3) = -2/5
Example Question #2 : Geometry
Which of the following lines intersects the y-axis at a thirty degree angle?
y = x - √2
y = x
y = x√3 + 2
y = x√2 - 2
y = x((√3)/3) + 1
y = x√3 + 2
Example Question #5 : How To Find Slope Of A Line
What is a possible slope of line y?
2
–2
–2
The slope is negative as it starts in quadrant 2 and ends in quadrant 4. Slope is equivlent to the change in y divided by the change in x. The change in y is greater than the change in x, which implies that the slope must be less than –1, leaving –2 as the only possible solution.
Example Question #2 : Coordinate Geometry
What is the slope between 
Let 
Example Question #3 : Coordinate Geometry
Example Question #4 : Coordinate Geometry
Refer to above red line. What is its slope?
The slope of a line. given two points 
Set 
Example Question #1 : Coordinate Geometry
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 : Psat Mathematics
Solve the equation for x and y.
–x – 4y = 245
5x + 2y = 150
x = 545/9
y = –1375/18
x = 234/5
y = 1245/15
x = –1375/9
y = 545/18
x = 3
y = 7
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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