Chapter Test
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To find the equation of line q, you need to know two points through which the line passes.
What can you say about the slope of line p compared to line q?
By setting the equations of the lines equal to each other, you can solve for the x-coordinate where the lines intersect.
Use the Distance Formula.
y=- 3x+13
y=1/3x+3
(3,4)
About 316 yards.
Let's draw the diagram, labeling the coordinates for the aquarium, shopping mall, and subway.
Line q is a linear function and can therefore be written in slope-intercept form
Substitute ( 4,1) & ( 2,7)
Subtract terms
Calculate quotient
When we have the slope, we can solve for the y-intercept, b, by substituting one of the known points into the slope-intercept form.
The equation of line q is y=- 3x+13.
From the diagram, we see that line p intersects the y-axis at (0,3). This means it has a y-intercept of 3. So far, we can write the equation for line p as
y=mx+3.
m_1= - 3
LHS * (- 1)=RHS* (- 1)
.LHS /3.=.RHS /3.
The equation of line p is y= 13x+3.
To find the coordinates of the meeting point, we set the equations of line p and q equal to each other and solve for x
The lines intersect at x=3. We can find the corresponding y-coordinate if we substitute our value of x into one of the equations, and solve for y.
The meeting point is at (3,4).
From the coordinate plane, we see that the segment between the meeting point and the subway has endpoints at (3,4) and (9,6). Using the Distance Formula, we can find the distance of this segment.
Substitute ( 9,6) & ( 3,4)
The distance from the meeting point to the subway is sqrt(40). By multiplying this distance by 50, we get the total distance in yards: 50* sqrt(40)≈ 316 yards.