Solve the following system of equations graphically on the set of axes below. y = x - 3 y = - 3/5x + 5
1 answer:
Answer:
Solution by graphing: (5, 2)
Step-by-step explanation:
y = x - 3
y = - 3/5x + 5
To solve systems of linear equations graphically, you'll have graph each equation using 2 pairs of points.
A great starting point is always using its intercepts:
y = x - 3
where the y-intercept is (0, -3).
To find its x-intercept, set y = 0 and solve for the value of x:
y = x - 3
0 = x - 3
Add 3 to both sides:
0 + 3 = x - 3 + 3
3 = x
Therefore, the x-intercept = (3, 0).
y = - 3/5x + 5
where the y-intercept is (0, 5).
Next, you could find a value of x that easily cancels out the fraction given by the slope (m) = -3/5. An input value of x = 5 cancels out the denominator of the slope:
y = - 3/5x + 5
y = - 3/5(5) + 5
y = -3 + 5
y = 2
Therefore, the other point that you could use to plot on the graph is (5, 2).
For y = x - 3, we'll use the line's intercepts: (0, -3) and (3, 0).
For y = - 3/5x + 5, we'll use (0, 5) and (5, 2).
Plotting these points on the graph will give us a solution of (5, 2), as it is the <u>point where both lines intersect</u>. Attached is a screenshot of the graphed lines.
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Step-by-step explanation:
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Answer: I'm not going to give out the answers but I'm happy to explain it and help you out if you're still confused. I'm a geometry honors student rn btw just so you know my credentials.
Step-by-step explanation:
To find slope and write it in slope-intercept form you first need to know the equation and what different variables represent.
y = mx + b is the equation for slope-intercept. You need to find what m and b are to right a slope-intercept equation. for example the first problem's answer is y = x + 1
m is slope which is the angle that the line is at. To find slope or m, you need to choose a point on the graph. Then, count the amount of spaces vertically and horizontally until the next point on the graph. When I say point, I'm referring to a place on the graph where the line cross perfectly over the intersection of two lines on the graph. Slope is always 'rise over run' meaning it is a fraction containing the amount up or down, over the amount left or right. For example, the first problem (the one on the top left) the slope is .
b is the y-intercept. The y intercept where the line crosses the y-axis which is that bold line going up and down in the middle. For example in number one, the y-intercept is 1 because it is one unit up from the origin. (the origin is 0,0, or the very middle of the graph).
Hope this helps! :)