Question

y = 2x - 3
option 1 option 2
option 3 option 4

Explanation:

Step1: Analyze the slope

The equation is \( y = 2x - 3 \). The slope \( m = 2 \), which is positive, so the line should be increasing (going up from left to right). Option 1 and Option 3 have negative slopes (decreasing), so we eliminate them.

Step2: Analyze the y-intercept

The y-intercept \( b = -3 \), so the line crosses the y-axis at \( (0, -3) \). Let's check Option 2 and Option 4. Option 2: When \( x = 0 \), \( y = -3 \)? Wait, no, looking at Option 2's graph, the y-intercept seems to be around \( -3 \)? Wait, no, let's check the points. Wait, Option 4: Let's plug \( x = 0 \), \( y = -3 \). Let's check the slope. For Option 4, let's take two points. When \( x = 1 \), \( y = 2(1) - 3 = -1 \). So the point \( (1, -1) \) should be on the line. Option 4's graph: when \( x = 1 \), \( y = -1 \)? Wait, no, maybe I made a mistake. Wait, the equation is \( y = 2x - 3 \). Let's find two points. When \( x = 0 \), \( y = -3 \) (y-intercept). When \( x = 1 \), \( y = 2(1) - 3 = -1 \). When \( x = 2 \), \( y = 1 \). Now let's check the options. Option 2: The line has a positive slope, y-intercept at \( -3 \)? Wait, no, Option 2's graph: when \( x = 0 \), the y-value is -3? Wait, the grid: each square is 1 unit. Let's look at Option 4: when \( x = 0 \), \( y = -3 \), and when \( x = 1 \), \( y = -1 \), which matches \( y = 2x - 3 \). Option 2: Let's see, when \( x = 0 \), the y-intercept is -3? Wait, no, maybe I messed up. Wait, the slope is 2, so for each increase in x by 1, y increases by 2. So from \( (0, -3) \), moving right 1 (x=1), y should be -1 (up 2 from -3). So the point \( (1, -1) \). Let's check Option 4: yes, that point is on it. Option 2: Let's see, when x=0, y is -3? Wait, Option 2's graph: the line is going through (0, -3)? Wait, no, maybe the options are labeled differently. Wait, the original problem: Option 4's graph: when x=0, y=-3, and the slope is 2 (positive, increasing). So Option 4 is correct. Wait, no, maybe I made a mistake. Wait, let's re-express:

Equation: \( y = 2x - 3 \).

Slope: positive (2), so line goes up from left to right. Eliminate Option 1 (negative slope) and Option 3 (negative slope).

Now between Option 2 and Option 4.

Y-intercept: (0, -3). Let's check Option 2: when x=0, the y-coordinate is -3? Wait, Option 2's graph: the line crosses the y-axis at (0, -3)? Wait, no, looking at the graph, Option 2's line at x=0 is at y=-3? Wait, maybe the correct option is Option 4. Wait, no, let's check the points again.

Wait, maybe I made a mistake in Option 2. Let's take x=0: y=-3. x=1: y=-1. x=2: y=1. So the line should pass through (0, -3), (1, -1), (2, 1). Now look at Option 4: yes, those points are on it. Option 2: Let's see, when x=0, the y-intercept is -3? Wait, the graph of Option 2: the line is below the x-axis, with positive slope. Wait, maybe the correct answer is Option 4.

Wait, maybe I messed up the initial elimination. Let's recheck:

Option 1: negative slope (decreasing) – eliminate (slope is 2, positive).

Option 3: negative slope (decreasing) – eliminate.

Option 2: positive slope, but let's check the y-intercept. When x=0, y=-3? Wait, the graph of Option 2: the line crosses the y-axis at (0, -3)? Wait, no, looking at the grid, each square is 1 unit. Option 2's line at x=0 is at y=-3? Wait, maybe. But let's check the slope. For Option 2, take two points: (0, -3) and (1, -1) – slope is 2, which matches. Wait, but Option 4: (0, -3) and (1, -1) – also slope 2. Wait, maybe the difference is in the direction. Wait, no, both have positive slopes. Wait, maybe the original graph's Option 4 is the correct one. Wait, maybe I made a mistake. Wait, the equation is \( y = 2x - 3 \). Let's plot the points:

- (0, -3)

- (1, -1)

- (2, 1)

- (3, 3)

Now look at Option 4: the line passes through (0, -3), (1, -1), (2, 1), (3, 3) – yes, that's correct. Option 2: Let's see, the line in Option 2: when x=0, y=-3? Wait, no, maybe the y-intercept in Option 2 is -3, but the slope is 1? Wait, no, the slope should be 2. Wait, maybe the correct option is Option 4.

Answer:

Option 4