Final answer:
To write a slope-intercept form equation for a line parallel to y = -3/4x + 4 that passes through (-2,3), we use the same slope of -3/4. Substituting the point into the slope-intercept form and solving for the y-intercept gives us the new equation: y = -3/4x + 3/2.
Step-by-step explanation:
The student asked to write an equation in slope-intercept form for a line that is parallel to the given equation y = -3/4x + 4 and passes through the point (-2,3). To find the equation of a line that is parallel to another, we need to use the same slope because parallel lines have the same slope. The slope mentioned in the provided equation is -3/4, hence the new line will also have this slope.
Now, using the point (-2,3) and the slope -3/4, we can use the slope-intercept form, which is y = mx + b, where m is the slope and b is the y-intercept, to find the new y-intercept. Plugging in the coordinates of the point and the slope:
y = -3/4x + b
3 = (-3/4)(-2) + b
3 = 3/2 + b
b = 3 - 3/2
b = 3/2
Finally, our new equation is:
y = -3/4x + 3/2
This new line will be parallel to the given line and pass through the specified point.