<p>From the Mathematics Section of the blue book:(Page 368 in my older edition)</p>
<p>Which of the following is an equation of the line that has a y-intercept of 2 and an x-intercept of 3?</p>
<p>So far I tried . . .</p>
<p>1) y = mx + b
y = mx + 2</p>
<p>2) (y-y1) = m(x-x1) point-slope form
y - 2 = m(x - 0)
y - mx = 2</p>
<p>Not getting anywhere. How do I solve this problem?</p>
<p>To solve this problem, imagine the graph in your head. So far, we have a point at (0,2), and a point at (3,0). So we know just by imagining this that the graph is consistently decreasing. In 7th grade algebra this year, one of the methods I learned to find the slope of a graph is to do this: find the change between the points and then divide the change in y by the change in x. For example: in the first point, x is 0, in the next point, x is 3. So there was a change of +3 in x. In the first point for y, y was 2, in the next point, y was 0. So there was a change of -2. Now we divide the change in y by the change in x. So the slope is -2/3. Now we just plug in the slope to y=mx+b form</p>
<p>y=-2/3x+2</p>
<p>Because I kinda suck at explaining things, here is a link to show what I mean: [Slope</a> of a Straight Line](<a href=“http://www.purplemath.com/modules/slope.htm]Slope”>The Slope of a Straight Line | Purplemath)</p>
<p>Not super confident in my answer, but whatever.
y intercept 2: (0,2)
x intercept 3: (3,0)
slope: (y2-y1)/(x2-x1) (2-0)/(0-3) = -2/3
Plug it into y = mx + b; y = -2/3x + 2</p>
<p>Again, I could be totally wrong.</p>
<p>The solutions mentioned above are correct. Here’s how I tackled this problem.</p>
<p>Convert the x and y intercepts into points on a coordinate plane.</p>
<p>y intercept of 2 = (0,2)
x intercept of 3 = (3,0)</p>
<p>Equation of a line: y = mx + b
b= y coordinate of the y intercept. Thus, b = 2 and we get:
y = mx + 2</p>
<p>To find m, plug in the coordinates of the x intercept. y = 0. x = 3</p>
<p>0 = 3m + 2
Solution becomes m = -2/3</p>
<p>Combine all parts and you get your final equation: y = -2/3x + 2</p>
<p>Hope that helped.</p>