SAT Math : Geometry
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Example Question #11 : How To Find Out If A Point Is On A Line With An Equation
Figure NOT drawn to scale.
On the coordinate axes shown above, the shaded triangle has the following area:
Evaluate 
The lengths of the horizontal and vertical legs of the triangle correspond to the 
Therefore, the 
substituting:
Substituting for 
the line has equation
Substituting 
of the point on the line with 
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
–9
–11
–10
–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 #2 : Slope And Line Equations
What is the slope of a line that runs through points: (-2, 5) and (1, 7)?
2/3
3/2
5/7
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 #1 : Psat Mathematics
A line passes through the points (–3, 5) and (2, 3). What is the slope of this line?
–2/5
2/3
2/5
-3/5
–2/3
–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 : Geometry
What is the slope between 
Let 
Example Question #3 : How To Find The Slope Of A Line
What is the slope of line 3 = 8y - 4x?
0.5
-0.5
2
-2
0.5
Solve equation for y. y=mx+b, where m is the slope
Example Question #31 : Lines
Find the slope of the line 6X – 2Y = 14
12
-3
3
-6
3
Put the equation in slope-intercept form:
y = mx + b
-2y = -6x +14
y = 3x – 7
The slope of the line is represented by M; therefore the slope of the line is 3.
Example Question #4 : How To Find The Slope Of A Line
If 2x – 4y = 10, what is the slope of the line?
–2
0.5
2
–5/2
–0.5
0.5
First put the equation into slope-intercept form, solving for y: 2x – 4y = 10 → –4y = –2x + 10 → y = 1/2*x – 5/2. So the slope is 1/2.
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