Question

A line passes through the point (4,1) and has a slope of -3/2 . Write an equation in slope-intercept form for this line.

Answer 1

The equation of the line in slope-intercept form that passes through the point (4,1) with a slope of -3/2 is y = (-3/2)x + 7.

Step-by-step explanation:

The student asked for an equation of a line in slope-intercept form that passes through the point (4,1) with a slope of -3/2. The slope-intercept form of a line is expressed as y = mx + b, where m is the slope and b is the y-intercept. Given that we have a point and a slope, we can use the point-slope form y - y1 = m(x - x1) to plug in our values and then solve for y to put it into slope-intercept form.

Starting with the point-slope form:

y - 1 = (-3/2)(x - 4)

We distribute the slope on the right-hand side:

y - 1 = (-3/2)x + 6

Add 1 to both sides to isolate y:

y = (-3/2)x + 7

Now, we have the line's equation in slope-intercept form where the slope is -3/2 and the y-intercept is 7.

Answer 2

y=mx+b is the equation of a line;

m=slope , b= y-intercept

m= -3/2 ; so we have : y= (-3/2)x+b

We are give a set of points which it passes through, we can simply plug them in:

1 = (-3/2)(4)+b (4 is the x and 1 is the y)

We get 1 = -6 +b .... 7=b

our final equation is : y=(-3/2)x+7