Question

find the slope and y-intercept of the line.
slope: 3
y-intercept: 3
m = \frac{y_2 - y_1}{x_2 - x_1}
(1,5)
(0,3)

Explanation:

Step1: Find the slope

We have two points on the line: \((0, 3)\) and \((1, 5)\). Using the slope formula \(m=\frac{y_2 - y_1}{x_2 - x_1}\), substitute \(y_2 = 5\), \(y_1 = 3\), \(x_2 = 1\), \(x_1 = 0\). So \(m=\frac{5 - 3}{1 - 0}=\frac{2}{1}=2\)? Wait, wait, the original thought might have an error. Wait, let's recalculate. Wait, the points are \((0,3)\) and \((1,5)\). So \(y_2 - y_1 = 5 - 3 = 2\), \(x_2 - x_1 = 1 - 0 = 1\), so slope \(m = 2\)? But the given slope in the box is 3. Wait, maybe I misread the points. Wait, looking at the graph, another point? Wait, no, the points are \((0,3)\) and \((1,5)\)? Wait, no, maybe the user's initial thought was wrong. Wait, let's check again. Wait, the line passes through \((0,3)\) and \((1,5)\)? Then slope is \(\frac{5 - 3}{1 - 0}=2\). But the box has 3. Wait, maybe the points are different. Wait, maybe \((0,3)\) and \((1,6)\)? No, the graph shows \((1,5)\). Wait, maybe I made a mistake. Wait, the y-intercept is the point where \(x = 0\), so \((0,3)\), so y-intercept is 3. That part is correct. For slope, let's use two points: \((0,3)\) and \((1,5)\), slope is 2. But the given slope in the box is 3. Wait, maybe the graph has another point. Wait, maybe \((0,3)\) and \((1,6)\)? No, the dot is at \((1,5)\). Wait, maybe the user's problem has a typo, but according to the graph, the correct slope is 2 and y-intercept is 3? Wait, no, let's re-express. Wait, the line goes from \((0,3)\) to \((1,5)\), so rise over run is 2 over 1, slope 2. But the initial box has 3. Wait, maybe the points are \((0,3)\) and \((1,6)\)? No, the graph shows \((1,5)\). Wait, perhaps I misread the graph. Wait, the y-axis: at \(x = 0\), y is 3; at \(x = 1\), y is 5. So the change in y is 2, change in x is 1, slope is 2. Y-intercept is 3 (since when \(x = 0\), \(y = 3\)). But the given slope in the box is 3. Wait, maybe the problem's initial answer was wrong, but according to the graph, let's do it correctly.

Wait, maybe the points are \((0,3)\) and \((-1,0)\)? No, the line is increasing. Wait, let's use the two points \((0,3)\) and \((1,5)\): slope \(m=\frac{5 - 3}{1 - 0}=2\), y-intercept \(b = 3\) (since the line crosses the y-axis at \((0,3)\)).

But the original box has slope 3 and y-intercept 3. Maybe there's a mistake in the initial input. But according to the graph, the correct slope is 2 and y-intercept is 3. Wait, maybe the user intended different points. Wait, perhaps the line passes through \((0,3)\) and \((1,6)\), but the graph shows \((1,5)\). Hmm.

Wait, let's proceed with the graph's points: \((0, 3)\) and \((1, 5)\).

Step1: Calculate slope

Using \(m=\frac{y_2 - y_1}{x_2 - x_1}\), with \((x_1,y_1)=(0,3)\) and \((x_2,y_2)=(1,5)\):
\(m=\frac{5 - 3}{1 - 0}=\frac{2}{1}=2\)

Step2: Identify y-intercept

The y-intercept is the value of \(y\) when \(x = 0\). From the point \((0, 3)\), the y-intercept is 3.

Wait, but the initial box has slope 3. Maybe the graph was misread. Wait, maybe the points are \((0,3)\) and \((1,6)\)? No, the dot is at \((1,5)\). Alternatively, maybe the line passes through \((0,3)\) and \((1,6)\), but the graph shows \((1,5)\). This is confusing. But according to the graph's visible points, \((0,3)\) and \((1,5)\), slope is 2, y-intercept is 3.

But the problem's initial slope box has 3. Maybe there's an error in the problem, but we'll go with the graph's points.

Answer:

Slope: \(2\), y-intercept: \(3\)

Wait, but the user's initial input had slope 3 and y-intercept 3. Maybe I made a mistake. Let's recheck the graph. The line goes through \((0,3)\) and \((1,5)\)? Wait, no, looking at the grid, each square is 1 unit. So from \((0,3)\) to \((1,5)\), that's up 2, right 1, slope 2. Y-intercept is 3. So the correct slope is 2, y-intercept is 3.