Question

Pls help im struggling

Answer 1

Explanation:

Start of with the first one. Y=-x+3. The rule is to always start with b as in y=mx+b. The b is on the y axis so you start off with that. In this case there is a 3 so plot 3 on the graph. X stands for 1. In this case -1. So go down 1 from the 3 you just plotted. When the number is whole go right. So from the 3 go down 1 then right 1 and so one. If you lose space do the opposite. Go up 1 then left one and so one until you run out of room. Same this with the second one.

Start with b in this case -5 on the y axis. Go down -5. Then plot it and go up 5 from there and right 3 since they're both positive numbers.

Answer 2

(x, y) = (3, 0)

Explanation:

You want a graph and the solution to the system of equations ...

• y = -x +3
• y = 5/3x -5

Slope-intercept form

The slope-intercept form of the equation for a line is ...

y = mx + b . . . . . slope = m, y-intercept = b

You can see that the given equations are in this form.

The first line has a slope of m = -1 and a y-intercept of b = 3.

The second line has a slope of m = 5/3 and a y-intercept of b = -5.

Graph

The y-intercept in each case identifies a point on the y-axis that is one of the points on the line.

The slope is the ratio of "rise" to "run" for the line. This can be used to find another point on the line that can be used for graphing.

y = -x +3

The purple line in the attachment goes through two points, (0, 3) and (1, 2). The latter point is 1 unit down and 1 unit to the right of the y-intercept. That is, its "rise" is -1, and its "run" is +1, so m = rise/run = -1/1 = -1, as we noted above.

y = 5/3x -5

The green line in the attachment goes through the two points (0, -5) and (3, 0). The latter point is 5 units up (rise = 5) and 3 units right (run = 3) of the y-intercept point. We choose these values from the slope:

m = rise/run = 5/3 . . . . as noted above

Solution

The two lines intersect at the point (3, 0), so that is the solution to the system of equations:

(x, y) = (3, 0)

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