Given the linear equation y=-3/2x+1, find the y-coordinates of the points
(-4), (-2), and (6). Please show all of your work. Plot those points and graph the linear equation.
Points are written in the form (x,y), that is , they must have two values.
(-4) is not a point.
Do you mean, find the y value given that x = -4 ?
in that case,
y = (-3/2)(-4) + 1
= 6 + 1
= 7
so the first point is (-4,7)
do the others in the same way.
Thank you.
To find the y-coordinates of the points (-4), (-2), and (6) for the given linear equation y = -3/2x + 1, we can substitute the x-values into the equation and solve for y.
1. For x = -4:
y = -3/2(-4) + 1
y = 6 + 1
y = 7
Hence, the y-coordinate for x = -4 is 7.
2. For x = -2:
y = -3/2(-2) + 1
y = 3 + 1
y = 4
Therefore, the y-coordinate for x = -2 is 4.
3. For x = 6:
y = -3/2(6) + 1
y = -9 + 1
y = -8
Thus, the y-coordinate for x = 6 is -8.
To plot these points on the graph, we create a coordinate plane and mark the points (-4, 7), (-2, 4), and (6, -8).
Next, we can graph the linear equation y = -3/2x + 1 by using the slope-intercept form (y = mx + b), where m is the slope and b is the y-intercept.
From the given equation, we can see that the slope (m) is -3/2 and the y-intercept (b) is 1.
To graph it:
1. Plot the y-intercept: Start at the point (0, 1) on the y-axis.
2. Use the slope: From that point, move down 3 units and to the right 2 units to find the next point. Repeat this step to find more points.
Finally, connect the points on the graph to draw a straight line representing the linear equation.