Use the image to answer the question.
An illustration of a coordinate plane with four quadrants shows the x and y axes extending from negative 10 to 10 in increments of 1. A solid line and a dotted line with arrows at both the ends intersect each other. The equation of the solid line is y equals 5 x plus 10. The equation of the dotted line is y equals negative 2 x plus 3. The lines intersect at left parenthesis negative 1 comma 5 right parenthesis which is not plotted as a point.
Estimate the solution to the system of these linear equations based on the graph.
y=5x+10
y=−2x+3
(1 point)
Responses
(−1, 5)
left parenthesis negative 1 comma 5 right parenthesis
(5,−1)
left parenthesis 5 comma negative 1 right parenthesis
(−1,−5)
left parenthesis negative 1 comma negative 5 right parenthesis
(1, 5)
left parenthesis 1 comma 5 right parenthesis
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The correct answer is (-1, 5) or left parenthesis negative 1 comma 5 right parenthesis.
Based on the graph, the lines y=5x+10 and y=-2x+3 intersect at the point (-1, 5). Therefore, the estimated solution to the system of linear equations is (-1, 5).
To estimate the solution to the system of linear equations based on the graph, we need to find the point where the solid line and the dotted line intersect.
Looking at the equations, y = 5x + 10 and y = -2x + 3, we can see that they are both in the form y = mx + b, where m represents the slope and b represents the y-intercept.
For the solid line, y = 5x + 10, the slope is 5 and the y-intercept is 10. This means that for every 1 unit increase in x, y increases by 5.
For the dotted line, y = -2x + 3, the slope is -2 and the y-intercept is 3. This means that for every 1 unit increase in x, y decreases by 2.
Since the lines intersect at (-1, 5), we can conclude that this is the estimate for the solution to the system of linear equations based on the graph. Therefore, the correct response is (−1, 5) or left parenthesis negative 1 comma 5 right parenthesis.