12. Which equation represents the graph?%0D%0A%0D%0A%0D%0A%0D%0A(1 point)%0D%0AResponses%0D%0A%0D%0Ay=−45x+3%0D%0A%0D%0A=%0D%0A−%0D%0A4%0D%0A5%0D%0A%0D%0A+%0D%0A3%0D%0Ay is equal to negative 4 fifths x plus 3%0D%0A%0D%0Ay=12x−1%0D%0A%0D%0A=%0D%0A1%0D%0A2%0D%0A%0D%0A−%0D%0A1%0D%0Ay is equal to 1 half x minus 1%0D%0A%0D%0Ay=54x+3%0D%0A%0D%0A=%0D%0A5%0D%0A4%0D%0A%0D%0A+%0D%0A3%0D%0Ay is equal to 5 fourths x plus 3%0D%0A%0D%0Ay=3x+5
The equation that represents the graph is y = 3x + 5.
To determine which equation represents the given graph, we need to analyze the slope and y-intercept of the line.
The equation of a line can generally be written as y = mx + b, where m represents the slope and b represents the y-intercept.
Looking at the given options:
1. y = −45x + 3
2. y is equal to negative 4 fifths x plus 3
3. y = 12x − 1
4. y is equal to 1 half x minus 1
5. y = 54x + 3
6. y is equal to 5 fourths x plus 3
7. y = 3x + 5
By comparing the options with the given equation, y = 3x + 5, we can see that option 7 matches the given equation.
Therefore, the equation that represents the graph is y = 3x + 5.
To determine which equation represents the given graph, we can analyze the slope-intercept form of the equation, which is y = mx + b.
Let's compare the given equations one by one and see if they match the characteristics of the graph:
1. y = -45x + 3
The slope of this equation is -45, which means the graph will be a steep line. However, the graph given does not appear to be a steep line, so this equation does not represent the graph.
2. y = -4/5x + 3
The slope of this equation is -4/5, which indicates a negative slope that is less steep than the previous equation. The y-intercept is 3, meaning the graph intersects the y-axis at the point (0, 3). This equation could potentially represent the graph.
3. y = 12x - 1
The slope of this equation is 12, indicating a positive and steep slope. The y-intercept is -1, which means the graph intersects the y-axis at the point (0, -1). The graph given does not match the steep, positive slope depicted by this equation, so it does not represent the graph.
4. y = 1/2x - 1
The slope of this equation is 1/2, indicating a positive but less steep slope. The y-intercept is -1, meaning the graph intersects the y-axis at the point (0, -1). The given graph seems to have a similar slope and y-intercept, so this equation could represent the graph.
5. y = 54x + 3
The slope of this equation is 54, indicating a very steep positive slope. The y-intercept is 3, meaning the graph intersects the y-axis at the point (0, 3). However, the given graph does not match the extremely steep slope depicted by this equation, so it does not represent the graph.
Comparing the given graph to the equations, it appears that the equation y = 1/2x - 1 best represents the graph.